Final answer:
To construct a 99% confidence interval of the mean time it takes job seekers to find a new job, we can use the formula: μ ± z * (σ/√n). Given the average time, sample size, and standard deviation, we can calculate the confidence interval. The 99% confidence interval for the mean time it takes job seekers to find a new job is (5.5652, 6.2348) months.
Step-by-step explanation:
To construct a 99% confidence interval of the mean time it takes job seekers to find a new job, we can use the formula: μ ± z * (σ/√n), where μ is the population mean, σ is the standard deviation, n is the sample size, and z is the z-value for the desired confidence level.
Given that the average time is 5.9 months, the sample size is 36, and the standard deviation is 0.8 months, we can calculate the z-value using a standard normal distribution table or a statistical software. For a 99% confidence level, the z-value is approximately 2.576.
Substituting the values into the formula, we get the confidence interval: 5.9 ± 2.576 * (0.8/√36) = 5.9 ± 0.3348. Therefore, the 99% confidence interval for the mean time it takes job seekers to find a new job is (5.5652, 6.2348) months.